Janus MoSSe monolayer has been widely considered as an appealing anode for lithium-ion batteries (LIBs), owing to its suitable open circuit voltage, low diffusion barrier and high specific capacity. However, Janus MoSSe suffers from low electrical conductivity and poor mechanical property, resulting in a rapid capacity decay during cycling. Thus, in this work, we proposed two MoSSe/graphene (SMoSe/G and SeMoS/G) heterostructures as anodes of LIBs, which not only eliminate the drawbacks of MoSSe but also integrate the advantages of individual components. By means of first principles computations, we have systematically investigated the structural, electronic, mechanical and electrochemical properties of MoSSe/graphene heterostructures. Our results show that MoSSe/graphene heterostructures possess good structural stability, superior Li-ion conductivity and high mechanical stiffness (Yx(y),SMoSe/G=459.8 N/m; Yx(y),SeMoS/G = 459.3 N/m). Due to the synergistic effect between MoSSe and graphene, the adsorption energies of Li in heterostructures are much larger than those of pristine MoSSe and graphene. Accordingly, the MoSSe/G heterostructures achieve a high theoretical capacity of 560.59 mA h/g. Moreover, the diffusion barriers in SMoSe/G and SeMoS/G heterostructures are 0.17 and 0.22 eV, respectively, ensuring high mobility of Li. All these encouraging results demonstrate that the MoSSe/graphene heterostructures are high-performance anodes for advanced LIBs.